Given the difficulties of constructing the feature set and the slow training speed of the evaluation model when using the pattern recognition method for power system transient stability assessment, a power system transient stability assessment method based on Minimum Volume Enclosing Ellipsoid (MVEE) and Least Square Projection Twin Support Vector Machine (LSPTSVM) is proposed. First, according to the MVEE theory, the system trajectory information is optimized to determine the minimum volume closure ellipsoid with all trajectory information in high dimensional space. We construct the input feature set using the physical properties of the minimum volume closure ellipsoid. This can effectively achieve feature set dimension reduction. Secondly, a regularization term is introduced into the objective function of the traditional projection twin support vector machine, and the internal constraints of the evaluation model are improved. This can improve the solution speed of the model and meet the computational efficiency requirements of large-scale power systems. Finally, the validity and feasibility of the proposed method are verified by the case analysis of IEEE-39 and IEEE-145 node systems. This work is supported by Science and Technology Project of State Grid Corporation of China (No. SGTYHT17- JS-199) and Science and Technology Project of State Grid Liaoning Electric Power Co., Ltd. (No. SGTYHT17JS201).